Iris image data processing for use with iris recognition system

ABSTRACT

Disclosed is an iris recognition method which is one of biometric technologies. According to a non-contact-type human iris recognition method by correction of a rotated iris image, the iris image is acquired by image acquisition equipment using an infrared illuminator. Inner and outer boundaries of the iris are detected by analyzing differences in pixels of a Canny edge detector and the image for the inputted iris image, so as to allow the boundaries of the iris to be more accurately detected from the eye image of a user. Thus, the iris image with a variety of deformation can be processed into a correct iris image, so that there is an advantage in that a false acceptance rate and a false rejection rate can be markedly reduced.

RELATED APPLICATIONS

This application is a continuation application of Application No.10/656,921, which is a continuation application under 35 U.S.C. §365 (c)claiming the benefit of the filing date of PCT Application No.PCT/KR01/01302 designating the United States, filed Jul. 1, 2001. ThePCT Application was published in English as WO 02/071316 A1 on Sep. 12,2002, and claims the benefit of the earlier filing date of Korean PatentApplication No. 2001/11441, filed Mar. 6, 2001. The contents of theKorean Patent Application No. 2001/11441, the international applicationNo. PCT/KR01/01302 including the publication WO 02/071316 A1 andapplication Ser. No. 10/656,921 are incorporated herein by reference intheir entirety.

BACKGROUND

1. Field

The present disclosure relates to processing iris image data, and moreparticularly, to a method of identifying an outer boundary of an irisimage.

2. Discussion of the Related Art

An iris recognition system is an apparatus for identifying personalidentity by distinguishing one's own peculiar iris pattern. The irisrecognition system is superior in its accuracy in terms of the personalidentification in comparison to the other biometric methods such asvoice or fingerprint, and it has a high degree of security. The iris isa region existing between the pupil and the white sclera of an eye. Theiris recognition method is a technique for identifying personalidentities based on information obtained by analyzing respective one'sown iris patterns different from each other.

Generally, the kernel technique of the iris recognition system is toacquire a more accurate eye image by using image acquisition equipmentand to efficiently acquire unique characteristic information on the irisfrom the inputted eye image.

However, in a non-contact type human iris recognition system whichacquires an iris image to be taken at a certain distance therefrom, theiris image with a variety of deformation may be acquired in practical.That is, it is unlikely that a complete eye image can be acquired sincethe eye is not necessarily directed toward a front face of a camera butpositioned at a slight angle with respect to the camera. Thus, there maybe a case where the information on an eye image rotated at an arbitraryangle with respect to a centerline of the iris is acquired.

The foregoing discussion in the background section is to provide generalbackground information and does not constitute an admission of priorart.

SUMMARY

One aspect of the invention provides a method of processing iris imagedata, which comprises: providing data of an eye image comprising an irisdefined between an inner boundary and an outer boundary; providinginformation indicative of a center of the inner boundary, a first innerboundary pixel and a second inner boundary pixel, wherein the first andsecond inner boundary pixels are located on a first imagery line passingthe center; computing to locate a first outer boundary pixel on thefirst imaginary line extending outwardly from the first inner boundarypixel; computing to locate a second outer boundary pixel on the firstimaginary line extending outwardly from the second inner boundary pixel;and computing to locate a center of the outer boundary using the firstouter boundary pixel and the second outer boundary pixel.

In the foregoing method, computing to locate the center of the outerboundary may comprise computing a bisectional point of the first andsecond outer boundary pixels. The method may further comprise computinga first distance between the first inner boundary pixel and the firstouter boundary pixel. The method may further comprise obtaining adistance between the first inner boundary pixel and the second innerboundary pixel. Computing to locate the center of the outer boundary mayuse a first distance defined between the first inner boundary pixel andthe first outer boundary pixel and a second distance defined between thesecond inner boundary pixel and the second outer boundary pixel.Computing the center of the outer boundary may further use a distancebetween the first inner boundary pixel and the second inner boundarypixel. The center of outer boundary may be off the center of the innerboundary.

Still in the foregoing method, the method may further comprise:providing information indicative of a third inner boundary pixel and afourth inner boundary pixel, wherein portion to obtain a characteristicvector of a an iris pattern. Processing the data may further compriseobtaining a plurality of characteristic vectors for the same eye image.

Another aspect of the invention provides a method of processing irisimage data, which comprises: providing data of an eye image comprisingan iris defined between an inner boundary and an outer boundary;providing information indicative of a first inner boundary pixel, asecond inner boundary pixel, a third inner boundary pixel and a fourthinner boundary pixel, which are located at different positions on theinner boundary; computing to locate a first outer boundary pixel on afirst imaginary line extending generally radially from the first innerboundary pixel; computing to locate a second outer boundary pixel on asecond imaginary line extending generally radially from the second innerboundary pixel; computing to locate a third outer boundary pixel on athird imaginary line extending generally radially from the third innerboundary pixel; computing to locate a fourth outer boundary pixel on afourth imaginary line extending generally radially from the fourth innerboundary pixel; and using the first, second, third and fourth outerboundary pixels for further processing.

In the foregoing method, the method may further comprise computing tolocate a center of the outer boundary using the first, second, third andfourth outer boundary pixels. The first imaginary line may besubstantially perpendicular to the third and fourth imaginary lines, andwherein the second imaginary line may be substantially perpendicular tothe third and fourth imaginary lines. A pixel located on the firstimaginary line may be determined to be the first outer boundary pixelwhen the difference of the image information between the pixel and itsneighboring pixel which are located on the first imaginary line becomesthe maximum among differences of the image information between twoneighboring pixels located on the first imaginary line.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart explaining the procedures of a normalizationprocess of an iris image according to one embodiment of the presentinvention.

FIG. 2 a is a view showing a result of detection of a pupillary boundaryusing a Canny edge detector.

FIG. 2 b is a view showing center coordinates and diameter of a pupil.

FIG. 2 c shows an iris image upon obtainment of a radius and center ofan the third and fourth inner boundary pixels are located on a secondimagery line passing the center; computing to locate a third outerboundary pixel on the second imaginary line extending outwardly from thethird inner boundary pixel; and computing to locate a fourth outerboundary pixel on the second imaginary line extending outwardly from thefourth inner boundary pixel, wherein computing to locate the center ofthe outer boundary further uses the third outer boundary pixel and thefourth outer boundary pixel. The second imaginary line may besubstantially perpendicular to the first imaginary line. Computing tolocate the center of the outer boundary may comprise computing abisectional point of the first and second outer boundary pixels and abisectional point of the third and fourth outer boundary pixels.Computing to locate the center of the outer boundary may use a firstdistance defined between the first inner boundary pixel and the firstouter boundary pixel, a second distance defined between the second innerboundary pixel and the second outer boundary pixel, a third distancedefined between the third inner boundary pixel and the third outerboundary pixel and a fourth distance defined between the fourth innerboundary pixel and the fourth outer boundary pixel. Computing to locatethe center of the outer boundary may further use a distance between thefirst inner boundary pixel and the second inner boundary pixel.

Further in the foregoing method, the first imaginary line may comprise afirst line segment extending outwardly from the first inner boundarypixel and a second line segment extending outwardly from the secondinner boundary pixel, wherein a pixel located on the first line segmentmay be determined to be the first outer boundary pixel when thedifference of the image information between the pixel and itsneighboring pixel which are located on the first line segment becomesthe maximum among differences of the image information between twoneighboring pixels located on the first line segment, wherein a pixellocated on the second line segment may be determined to be the secondouter boundary pixel when the difference of the image informationbetween the pixel and its neighboring pixel which are located on thesecond line segment becomes the maximum among differences of the imageinformation between two neighboring pixels located on the second linesegment. Providing information indicative of a center of the innerboundary may comprise performing a Canny edge detection method using theeye image data. The method may further comprise: extracting data of aportion of the eye image that is located between the inner boundary andthe outer boundary; and processing the data of the outer boundary of aniris according to one embodiment of the present invention.

FIGS. 3( a) to (d) show the procedures of the normalization process of aslanted iris image.

FIGS. 4( a) and (b) show a rotated iris image resulting from the tiltingof the user's head.

FIGS. 5( a) and (b) show procedures of a correction process of therotated iris image shown in FIGS. 4( a) and (b).

DETAILED DESCRIPTION OF EMBODIMENTS

Hereinafter, various embodiments of the present invention will bedescribed in detail with reference to the accompanying drawings.

FIG. 1 is a flowchart explaining procedures of a normalization processof an iris image according to one embodiment of the present invention.Referring to FIG. 1, at step 110, an eye image is acquired by imageacquisition equipment using an infrared illuminator and a visible lightrejection filter. At this time, a reflective light is caused to begathered in the pupil of an eye so that information on the iris image isnot lost. At step 120, inner and outer boundaries of the iris aredetected in order to extract only an iris region from the acquired eyeimage, and the center of the detected inner and outer boundaries is set.Step 120 is performed by a method for detecting the inner and outerboundaries of the iris using differences in pixels of a Canny edgedetector and the image according to one embodiment of the presentinvention, which will be specifically explained below.

FIG. 2 a is a view showing a result of detection of a pupillaryboundary, i.e. the inner boundary of the iris, using the Canny edgedetector. Referring to FIG. 2 a, it is noted that only the pupillaryboundary is detected by employing the Canny edge detector. That is, asshown in FIG. 2 a, the inner boundary of the iris is detected by usingthe Canny edge detector that is a kind of boundary detecting filter. TheCanny edge detector smoothes an acquired image by using Gaussianfiltering and then detects a boundary by using a Sobel operator. TheGaussian filtering process can be expressed as the following Equation 1,and the used Sobel operator can be expressed as the following Equation2.

I _(G)(x, y)=G(x, y)×I(x, y)   [Equation 1]

$\begin{matrix}\begin{matrix}{S_{x} = {{{I\left\lbrack {i - 1} \right\rbrack}\left\lbrack {j + 1} \right\rbrack} + {2\; {{I\lbrack i\rbrack}\left\lbrack {j + 1} \right\rbrack}} + {{I\left\lbrack {i + 1} \right\rbrack}\left\lbrack {j + 1} \right\rbrack} -}} \\{{{{I\left\lbrack {i - 1} \right\rbrack}\left\lbrack {j - 1} \right\rbrack} - {2\; {{I\lbrack i\rbrack}\left\lbrack {j - 1} \right\rbrack}} - {{I\left\lbrack {i + 1} \right\rbrack}\left\lbrack {j - 1} \right\rbrack}}} \\{S_{y} = {{{I\left\lbrack {i + 1} \right\rbrack}\left\lbrack {j + 1} \right\rbrack} + {2\; {{I\left\lbrack {i + 1} \right\rbrack}\lbrack j\rbrack}} + {{I\left\lbrack {i + 1} \right\rbrack}\left\lbrack {j - 1} \right\rbrack} -}} \\{{{{I\left\lbrack {i - 1} \right\rbrack}\left\lbrack {j + 1} \right\rbrack} - {2\; {{I\left\lbrack {i - 1} \right\rbrack}\lbrack j\rbrack}} - {{I\left\lbrack {i - 1} \right\rbrack}\left\lbrack {j - 1} \right\rbrack}}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

In a case where the boundary detecting method employing the Canny edgedetector is used, even though a normal eye image is not acquired sincethe eye of a user is not directed toward a front face of a camera butpositioned at a slight angle with respect to the camera, the innerboundary of the iris, i.e. papillary boundary, can be correctly detectedand center coordinates and radius of the pupil can also be easilyobtained. FIG. 2 b shows the center coordinates and diameter of thepupil. Referring to FIG. 2 b, the pupil's radius is d/2, and the pupil'scenter coordinates are (x+d/2, y+d/2).

On the other hand, the outer boundary of the iris in the image can bedetected by comparing pixel values while proceeding upward and downwardand leftward and rightward from the pupillary boundary, i.e. the innerboundary of the iris, and by finding out maximum values of differencesin the pixel values. The detected maximum values are Max{I(x, y)−I(x‘1,y)}, Max{I(x, y)−I(x+1, y)}, Max{I(x, y)−I(x, y−1)}, and Max{I(x,y)−I(x, y+1)}, where I(x, y) is a pixel value of the image at a point of(x, y). The reason why the differences in the pixel values are obtainedwhile proceeding upward and downward and leftward and rightward from theinner boundary of the iris upon detection of the outer boundary of theiris in the image is to make the inner and outer centers different fromeach other. That is, in a case where a slanted iris image is acquired,since the pupil is located a little upward, downward, leftward orrightward of the image, the inner and outer centers can be setdifferently from each other.

FIG. 2 c shows an iris image upon obtainment of the radius and center ofthe outer boundary of the iris according to one embodiment of thepresent invention. In a case where an incomplete eye image is acquiredsince the eye is not directed toward the front face of the camera butpositioned at a slight angle with respect to the camera, a process ofsetting the centers of the inner/outer boundaries of the iris isrequired. First, values of distances R_(L), R_(R), R_(U) and R_(D) fromthe inner boundary to the left, right, upper and lower portions of theouter boundary, respectively, and a value of the radius RI of the innerboundary, i.e. pupillary boundary, are calculated. Then, the center ofthe outer boundary is obtained by finding out bisection points upwardand downward and leftward and rightward of the image using the abovecalculated values.

At step 130, iris patterns are detected only at predetermined portionsof the distances from the inner boundary to the outer boundary. At step140, the detected iris pattern is converted into an iris image in thepolar coordinates. At step 150, the converted iris image in the polarcoordinates is normalized to obtain an image having predetermineddimensions in its width and height.

The conversion of the extracted iris patterns into the iris image in thepolar coordinates can be expressed as the following Equation 3.

I(x(r, θ), y(r, θ))=>I(r, θ)   [Equation 3]

where θ is increased by 0.8 degrees, and r is calculated by using thesecond Cosine Rule from a distance between the outer center C_(O) andthe inner center C_(I) of the iris, the radius R_(O) of the outerboundary, and the value of θ. The iris patterns between the inner andouter boundaries of the iris are extracted using the r and θ. In orderto avoid changes in features of the iris according to variations in thesize of the pupil, when the iris image between the inner and outerboundaries of the iris is divided into 60 segments and the θ is variedby 0.8 degrees to represent 450 data, the iris image is finallynormalized into a 27000 segmented iris image (θ×r=450×60).

FIG. 3( a) shows the slanted iris image, and FIG. 3( b) is the irisimage in polar coordinates converted from the slanted iris image. It canbe seen from FIG. 3( b) that a lower portion of the converted iris imagein the polar coordinates is curved with an irregular shape. In addition,FIG. 3( c) shows an iris image having the dimensions of M pixels inwidth and N pixels in height, which is normalized from the irregularimage of the iris patterns. Hereinafter, the normalization process ofthe slanted iris image will be described with reference to FIGS. 3( a)to (c). In the portion corresponding to the distance between the innerand outer boundaries of the iris in FIG. 3( a), the iris patternsexisting at only a portion corresponding to X % of the distance betweenthe inner and outer boundaries of the iris are taken in order toeliminate interference from the illuminator and acquire a large amountof iris patterns. That is, when the inner and outer boundaries of theiris are detected, the iris patterns are taken and then converted intothose in the polar coordinates. However, in a case where reflectivelight from the illuminator is gathered on the iris, iris patternsexisting at only a portion corresponding to 60% of the distance from theinner boundary among the region from the inner boundary (pupillaryboundary) of the iris to the outer boundary can be picked up andconverted into those in the polar coordinates. The value of 60% selectedin this embodiment of the present invention was experimentallydetermined as a range in which a greatest deal of iris patterns can bepicked up while excluding the reflective light gathered on the iris.

In FIG. 3( b), the slanted iris image is converted into the iris imagein the polar coordinates. As shown in FIG. 3( b), when the iris patternsare converted into those in the polar coordinates, the lower portion ofthe converted iris pattern image in the polar coordinates is curved withan irregular shape. Thus, it is necessary to normalize the irregulariris pattern image. In FIG. 3( c), the irregular image of the irispatterns is normalized to obtain the iris image with the dimensions of Mpixels in width and N pixels in height.

For reference, the performance of the iris recognition system isevaluated by two factors: a false acceptance rate (FAR) and a falserejection rate (FRR). The FAR means the probability that the irisrecognition system incorrectly identifies an impostor as an enrollee andthus allows entrance of the impostor, and the FRR means the probabilitythat the iris recognition system incorrectly identifies the enrollee asan impostor and thus rejects entrance to the enrollee. According to oneembodiment of the present invention, when a pre-processing is made byemploying the method for detecting the boundaries of the iris and thenormalization of the slanted iris image, the FAR was reduced from 5.5%to 2.83% and the FRR is reduced from 5.0% to 2.0% as compared with theiris recognition system employing a conventional method for detectingthe boundaries of the iris.

Finally, at step 160, if the iris in the acquired eye image has beenrotated at an arbitrary angle with respect to a centerline of the iris,the arrays of pixels of the iris image information are moved andcompared in order to correct the rotated iris image.

FIGS. 4( a) to (b) show a rotated iris image resulting from the tiltingof the user's head. Upon acquisition of an iris image, the user's headmay be tilted a little toward the left or right, under which if the irisimage is acquired, the rotated iris image is obtained as shown in FIG.4( a). That is, if the eye image acquired at step 110 has been rotatedat an arbitrary angle with respect to a centerline of the eye, a processof correcting the rotated image is required. FIG. 4( a) shows the irisimage rotated by about 15 degrees in a clockwise or counterclockwisedirection with respect to the centerline of the eye. When the rotatediris image is converted into an image in the polar coordinates, the irispatterns in the converted image are shifted leftward of rightward asshown in FIG. 4( b), as compared with the normal iris pattern.

FIGS. 5( a) and (b) show procedures of the process of correcting therotated iris image shown in FIGS. 4( a) and (b). The process ofcorrecting the rotated iris image, which has resulted from the tiltingof the user's head, by comparing and moving the arrays of the iris imageinformation will be described below with reference to FIGS. 5( a) and(b).

Referring to FIG. 5( a), from the rotated iris image resulting from thetiling of the user's head, a plurality of arrays Array(n) of the irisimage are temporarily generated by means of shifts by an arbitrary anglewith respect to an Array(0) of the converted iris image in the polarcoordinates. That is, by shifting columns leftward or rightward of theArray(0) based on the Array(0) of the converted iris image in the polarcoordinates, 20 arrays of image information from Array(0) to Array(−10)and from Array(0) to Array(10) are temporarily generated.

In order to generate characteristic vectors of the iris corresponding tothe plurality of arrays of iris image that have been temporarilygenerated, wavelet transform is performed. The respective characteristicvectors generated by the wavelet transform are compared with previouslyregistered characteristic vectors to obtain similarities. Acharacteristic vector corresponding to the maximum similarity among theobtained similarities is accepted as the characteristic vector of theuser.

In other words, by generating the arrays Array(n) of image informationon the rotated image as mentioned above and performing the wavelettransform for the respective arrays of the image information as shownFIG. 5( b), the characteristic vectors f_(T)(n) of the iriscorresponding to the temporarily generated plurality of arrays Array(n)of the iris image are the generated. The characteristic vectors f_(T)(n)are generated from f_(T)(0) to f_(T)(10) and from f_(T)(0) tof_(T)(−10). The respective generated characteristic vectors f_(T)(n) arecompared with each of the characteristic vectors f_(R) of the enrolleesand thus similarities S_(n) are obtained. A characteristic vectorf_(T)(n) corresponding to the maximum similarity among the obtainedsimilarities S_(n) is considered as a resulted value in which therotation effect is corrected, and is accepted as the characteristicvector of the user's iris.

As described above, according to the non-contact type human irisrecognition method by the correction of the rotated iris image of oneembodiment of the present invention, there is an advantage in that bydetecting the inner and outer boundaries of the iris using thedifferences in pixels of the Canny edge detector and the image, theboundaries of the iris can be more correctly detected from the eye imageof the user.

Furthermore, according to the non-contact type human iris recognitionmethod of one embodiment of the present invention, if the iris in theeye image acquired by the image acquisition equipment has been rotatedat an arbitrary angle with respect to the centerline of the iris, therotated image is corrected into the normal iris image. Otherwise, if alower portion of the converted iris image in the polar coordinates iscurved and thus has an irregular shape due to the acquisition of theslanted iris image, the iris image is normalized in predetermineddimensions. Thus, there is another advantage in that the iris image witha variety of deformation is processed into data on a correct iris imageso as to markedly reduce a false acceptance rate and a false rejectionrate.

It should be noted that the above description exemplifies of thenon-contact type human iris recognition method by the correction of therotated iris image according to embodiments of the present invention,and the present invention is not limited thereto. A person skilled inthe art can make various modifications and changes to the embodiments ofthe present invention without departing from the technical spirit andscope of the present invention defined by the appended claims.

1. A method of processing iris image data, comprising: providing data of an eye image comprising an iris defined between an inner boundary and an outer boundary; providing information indicative of a center of the inner boundary, a first inner boundary pixel and a second inner boundary pixel, wherein the first and second inner boundary pixels are located on a first imagery line passing the center; computing to locate a first outer boundary pixel on the first imaginary line extending outwardly from the first inner boundary pixel; computing to locate a second outer boundary pixel on the first imaginary line extending outwardly from the second inner boundary pixel; and computing to locate a center of the outer boundary using the first outer boundary pixel and the second outer boundary pixel.
 2. The method of claim 1, wherein computing to locate the center of the outer boundary comprises computing a bisectional point of the first and second outer boundary pixels.
 3. The method of claim 1, further comprising computing a first distance between the first inner boundary pixel and the first outer boundary pixel.
 4. The method of claim 1, further comprising obtaining a distance between the first inner boundary pixel and the second inner boundary pixel.
 5. The method of claim 1, wherein computing to locate the center of the outer boundary uses a first distance defined between the first inner boundary pixel and the first outer boundary pixel and a second distance defined between the second inner boundary pixel and the second outer boundary pixel.
 6. The method of claim 5, wherein computing the center of the outer boundary further uses a distance between the first inner boundary pixel and the second inner boundary pixel.
 7. The method of claim 1, wherein the center of outer boundary is off the center of the inner boundary.
 8. The method of claim 1, further comprising: providing information indicative of a third inner boundary pixel and a fourth inner boundary pixel, wherein the third and fourth inner boundary pixels are located on a second imagery line passing the center; computing to locate a third outer boundary pixel on the second imaginary line extending outwardly from the third inner boundary pixel; and computing to locate a fourth outer boundary pixel on the second imaginary line extending outwardly from the fourth inner boundary pixel, wherein computing to locate the center of the outer boundary further uses the third outer boundary pixel and the fourth outer boundary pixel.
 9. The method of claim 8, wherein the second imaginary line is substantially perpendicular to the first imaginary line.
 10. The method of claim 8, wherein computing to locate the center of the outer boundary comprises computing a bisectional point of the first and second outer boundary pixels and a bisectional point of the third and fourth outer boundary pixels.
 11. The method of claim 8, wherein computing to locate the center of the outer boundary uses a first distance defined between the first inner boundary pixel and the first outer boundary pixel, a second distance defined between the second inner boundary pixel and the second outer boundary pixel, a third distance defined between the third inner boundary pixel and the third outer boundary pixel and a fourth distance defined between the fourth inner boundary pixel and the fourth outer boundary pixel.
 12. The method of claim 11, wherein computing to locate the center of the outer boundary further uses a distance between the first inner boundary pixel and the second inner boundary pixel.
 13. The method of claim 1, wherein the first imaginary line comprises a first line segment extending outwardly from the first inner boundary pixel and a second line segment extending outwardly from the second inner boundary pixel, wherein a pixel located on the first line segment is determined to be the first outer boundary pixel when the difference of the image information between the pixel and its neighboring pixel which are located on the first line segment becomes the maximum among differences of the image information between two neighboring pixels located on the first line segment, wherein a pixel located on the second line segment is determined to be the second outer boundary pixel when the difference of the image information between the pixel and its neighboring pixel which are located on the second line segment becomes the maximum among differences of the image information between two neighboring pixels located on the second line segment.
 14. The method of claim 1, wherein providing information indicative of a center of the inner boundary comprises performing a Canny edge detection method using the eye image data.
 15. The method of claim 1, further comprising: extracting data of a portion of the eye image that is located between the inner boundary and the outer boundary; and processing the data of the portion to obtain a characteristic vector of a an iris pattern.
 16. The method of claim 15, wherein processing the data further comprises obtaining a plurality of characteristic vectors for the same eye image.
 17. A method of processing iris image data, comprising: providing data of an eye image comprising an iris defined between an inner boundary and an outer boundary; providing information indicative of a first inner boundary pixel, a second inner boundary pixel, a third inner boundary pixel and a fourth inner boundary pixel, which are located at different positions on the inner boundary; computing to locate a first outer boundary pixel on a first imaginary line extending generally radially from the first inner boundary pixel; computing to locate a second outer boundary pixel on a second imaginary line extending generally radially from the second inner boundary pixel; computing to locate a third outer boundary pixel on a third imaginary line extending generally radially from the third inner boundary pixel; computing to locate a fourth outer boundary pixel on a fourth imaginary line extending generally radially from the fourth inner boundary pixel; and using the first, second, third and fourth outer boundary pixels for further processing.
 18. The method of claim 17, further comprising computing to locate a center of the outer boundary using the first, second, third and fourth outer boundary pixels.
 19. The method of claim 17, wherein the first imaginary line is substantially perpendicular to the third and fourth imaginary lines, and wherein the second imaginary line is substantially perpendicular to the third and fourth imaginary lines.
 20. The method of claim 17, wherein a pixel located on the first imaginary line is determined to be the first outer boundary pixel when the difference of the image information between the pixel and its neighboring pixel which are located on the first imaginary line becomes the maximum among differences of the image information between two neighboring pixels located on the first imaginary line. 